Banking of road || Inclination of road || Physics || Class 11 ||

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                    Banking of road

The maximum permissible velocity with which vehicle can go round a level curved road without skidding depends on the coefficient of friction (μ) between the tyres and the road The value of Î¼ decreases when road is smooth or tyres of the vehicle are worn out or the road is wet and so on. Thus force of friction is not a reliable source for providing the required centripetal force to the vehicle.

A safer course of action would be to raise outer edge of the curved road shove the inner edge. By doing so, a component of normal reaction of the road shall be spared to provide the centripetal force. This phenomenon of raising outer edge of the curved road above the inner edge is called banking of roads. It's facilitates vehicles to turn without slipping.

Three forces are acting on the vehicle as shown in Figure below. 

(i) Weight mg of the vehicle acting vertically downwards. 

(ii) Normal reaction R of the banked road acting upwards in a direction perpendicular to OA. 

(iii) Force of friction F between the banked road and the tyres, acting along AO. #himanshu swiz

R can be resolved into two rectangular components : (i) R cos Î¸, along vertically upward direction (ii) R sin Î¸, along the horizontal, towards the centre of the curved road. 

F can also be resolved into two rectangular components:

(i) F cos Î¸ along the horizontal, towards the centre of curved road.

(ii) F sin Î¸, along vertically downward direction.

As there is no acceleration along the vertical direction, the net force along this direction must be zero.

Therefore,

             R cos Î¸ = mg + F sin Î¸

 If v is velocity of the vehicle over the banked circular road of radius, then centripetal force required =m×v²/r. This is provided by the horizontal components of R and F as shown in figure at right. 

@himanshu chaudhary. 

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